Flying from Paris to London Heathrow - will we have to do immigration/passport control?

You are landing in a country for a day, so yes, you will need to clear customs and immigration. It varies depending on when and where you arrive, but a general average guide is an hour from the plane touching down to getting out of the airport.

You will go through immigration (aka passport control) because the UK is not part of the Schengen area. You will go through exit control in Paris and entry control in London, At London Heathrow this could take 30 minutes to 1 hour. If you are an non-EU/Schengen citizen, your passport will be stamped in both places.
You will not go through customs, because both France and the UK are in the EU (at least currently!). This means after you pick up your bags you exit via the blue EU door.

If you are travelling from central Paris to central London, I recommend the Eurostar trains instead. This is both faster (city centre to city centre) and a lot more comfortable than flying. In this case both French and UK passport control is done at Gare du Nord before you board the train.

Eurostar is faster and cheaper than flying.

We took Eurostar from Paris Nord to Saint Pancras last week. It took us about 15 minutes including filling out forms for three of us to exit France border control and enter the UK. It all happens on the French side before you board. Make sure you have the full address of your fist nights lodging if you plan to stay overnight.

We had an 11:15 am train. Our daughter had a similar experience at 7:15 am.

If you are staying in London for the night I also suggest the Eurostar.

FLYING

One hour from central Paris to either ORY or CDG
2 hours minimum security, check in, passport, (check luggage?), get to gate before it closes, more time at CDG or if you aren't familiar with that massive airport
One hour flight
One hour clearing passports, walking the long corridors of Heathrow (how many miles did somebody say it was?) (collect luggage?), plus one hour into your destination in Central London or so.

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so 1+2+1+1+1 = 6 hours door to door

OR

EUROSTAR
One hour check in includes check in, security, both British and French passport control
2:15 travel time on the train
15 minutes to get off the train and walk the ramp to the Customs door and you are in Central London.

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so 1+2:15+0:15 = 3:30 and you are in Central London

So put the 2 and a half hours in your back pocket and enjoy.

I second that - unless there is some compelling reason you have for flying from CDG to LHR, take the Eurostar instead.